Telecommunication networks are rapidly evolving towards fully digital transmission techniques for both voice and data. One of the first digital carriers was the 24-voice channel 1.544 Mb/s T1 system, introduced in the United States in approximately 1962. Due to advantages over more costly analog systems, the T1 system became widely deployed. An individual voice channel in the T1 system is generated by band limiting a voice signal in a frequency range from about 300 to 3400 Hz, sampling the limited signal at a rate of 8 kHz, and thereafter encoding the sampled signal with an 8 bit logarithmic quantizer. The resultant signal is a 64 kb/s digital signal. The T1 system multiplexes the 24 individual digital signals into a single data stream.
A T1 system limits the number of voice channels in a single grouping to 24. In order to increase the number of channels and still maintain a transmission rate of approximately 1.544 Mb/s, the individual signal transmission rate must be reduced from a rate of 64 kb/s. One method used to reduce this rate is known as transform coding.
In transform coding of speech signals, the individual speech signal is divided into sequential blocks of speech samples. The samples in each block are thereafter arranged in a vector and transformed from the time domain to an alternate domain, such as the frequency domain. Transforming the block of samples to the frequency domain creates a set of transform coefficients having varying degrees of amplitude. Each coefficient is independently quantized and transmitted. On the receiving end, the samples are de-quantized and transformed back into the time domain. The importance of the transformation is that the signal representation in the transform domain reduces the amount of redundant information, i.e. there is less correlation between samples. Consequently, fewer bits are needed to quantize a given sample block with respect to a given error measure (e.g. mean square error distortion) than the number of bits which would be required to quantize the same block in the original time domain.
An example of such a prior transform coding system is shown in greater detail in FIG. 1. A speech signal is provided to a buffer 10, which arranges a predetermined number of successive samples into a vector x. Vector x is linearly transformed from the time domain to an alternate domain using a unitary matrix A by transform member 12, resulting in vector y. The elements of vector y are quantized by quantizer 14, yielding vector Y, which vector is transmitted. Vector Y is received and de-quantized by de-quantizer 16, and transformed back to the time domain by inverse transform member 18, using the inverse matrix A.sup.-1. The resulting block of time domain samples are placed back into successive sequence by buffer 20. The output of buffer 20 is ideally the reconstructed original signal.
While the transform coding scheme in theory provided satisfaction of the need to reduce the bit rate of individual T1 channels, historically the quantization process produced unacceptable amounts of noise and distortion. To a large extent, the noise and distortion problems emanated from two areas: the inability of various transform matrices to efficiently transform the original signal; and from the distortion and noise created in the quantization process.
In an attempt to optimize transform efficiency, various transform matrices have been evaluated. It is generally agreed that the optimal transform matrix is the Karhunen-Loeve Transform (KLT). The problem with this transform, however, is that it lacks a fast computation algorithm and the matrix is signal-dependent. Consequently, other transforms have been investigated, for example, the Walsh-Hadamard Transform (WHT), the discrete slant transform (DST), the discrete Fourier Transform (DFT), the symmetric discrete Fourier Transform (SDFT), and the discrete cosine transform (DCT). The SDFT and DCT appear to be closest in efficiency to the KLT, are signal-independent and include fast algorithms.
In attempting to resolve the distortion and noise problems, previous investigations centered on the quantization process. Quantization is the procedure whereby an analog signal i converted to digital form. Max, Joel "Quantization for Minimum Distortion" IRE Transactions on Information Theory, Vol. IT-6 (March, 1960), pp. 7-12 (MAX) discusses this procedure. In quantization the amplitude of a signal is represented by a finite number of output levels. Each level has a distinct digital representation. Since each level encompasses all amplitudes falling within that level, the resultant digital signal does not precisely reflect the original analog signal. The difference between the analog and digital signals is the quantization noise. Consider for example the uniform quantization of the signal x, where x is any real number between 0.00 and 10.00, and where five output levels are available, at 1.00, 3.00, 5.00, 7.00 and 9.00, respectively. The digital signal representative of the first level in this example can signify any real number between 0.00 and 2.00. For a given range of input signals, it can be seen that the quantization noise produced is inversely proportional to the number of output levels. In early quantization investigations for transform coding, it was found that not all transform coefficients were being quantized and transmitted at low bit rates.
Initial quantization investigations involved quantizers having logarithmic characteristics and having bit assignment schemes which were used to determine the optimum number of bits to be assigned by the quantizer to a given sample block containing a number of transform coefficients. Such schemes utilized formulae which took into account an averaged mean-squared distortion of the transformed signal over long periods. Approaches of this type were deemed to be fixed bit allocation processes because bit assignment and step-size are fixed a priori and are based upon long term speech statistics. As indicated above, a major problem which occurred at lower bit rates was the lack of a sufficient number of bits to quantize all of the speech samples or coefficients in each block. Some speech samples were lost. Consequently, distortion noise utilizing these schemes remained unsatisfactory at lower bit rates.
Further attempts to improve the transform coding distortion noise problem at lower bit rates, involved investigating the quantization process using dynamic bit assignment and dynamic step-size determination processes. Bit assignment was adapted to short term statistics of the speech signal, namely statistics which occurred from block to block, and step-size was adapted to the transform's spectral information for each block. These techniques became known as adaptive transform coding methods.
In adaptive transform coding, optimum bit assignment and step-size are determined for each sample block usually by adaptive algorithms which require certain knowledge about the variance of the amplitude of the transform coefficients in each block. The spectral envelope is that envelope formed by the variances of the transform coefficients in each sample block. Knowing the spectral envelope in each block, thus allows a more optimal selection of step size and bit allocation, yielding a more precisely quantized signal having less distortion and noise.
Since variance or spectral envelope information is developed to assist in the quantization process, this same information will be necessary in the de-quantization process. Consequently, in addition to transmitting the quantized transform coefficients, adaptive transform coding also provides for the transmission of the variance or spectral envelope. This is referred to as side information. Since the overall objective in adaptive transform coding is to reduce bit rate, the actual variance information is not transmitted as side information, but rather, information from which the spectral envelope may be determined is transmitted.
The spectral envelope represents in the transform domain the dynamic properties of speech, namely formants. Speech is produced by generating an excitation signal which is either periodic (voiced sounds), aperiodic (unvoiced sounds), or a mixture (eg. voiced fricatives). The periodic component of the excitation signal is known as the pitch. During speech the excitation signal is filtered by a vocal tract filter, determined by the position of the mouth, jaw, lips, nasal cavity, etc. This filter has resonances or formants which determine the nature of the sound being heard. The vocal tract filter provides an envelope to the excitation signal. Since this envelope contains the filter formants, it is known as the formant or spectral envelope.
Speech production can be modeled whereby speech characteristics are mathematically represented by convolving the excitation signal and vocal tract filter. In such a model, the vocal tract filter frequency response, i.e. the spectral envelope, is an estimate of the variance of the transform coefficients of the speech signal in the frequency domain. Hence, the more precise the determination of the spectral envelope, the more optimal the step-size and bit allocation determinations used to code transformed speech signals. Thus, adaptive transform coding techniques appear capable of efficiently coding and transmitting individual voice signals at lower bit rates.
In view of the above, adaptive transform coding research has concentrated on various techniques for more precisely determining the spectral envelope. One early technique disclosed in Zelinski, R. et al. "Adaptive Transform Coding of Speech Signals" IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. ASSP-25, No. 4 (August, 1977), pp. 299-309 and Zelinski, R. et al. "Approaches to Adaptive Transform Speech Coding at Low Bit Rates" IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. ASSP-27, No. 1 (February, 1979), pp. 89-95 involved estimation of the spectral envelope by squaring the transform coefficients, and averaging the coefficients over a preselected number of neighboring coefficients. The magnitude of the averaged coefficients were themselves quantized and transmitted with the coded signal as side information. To obtain the spectral estimates of all coefficients, the averaged coefficients were geometrically interpolated (i.e. linearly interpolated in the log domain). The result was a piecewise approximation of the spectral levels, i.e. variances, in the frequency domain. These values were then used by the bit assignment and step-size algorithms.
While it demonstrated acceptable distortion and noise at bit rates lower than 64 kb/s, the problem with this early technique was that it had a limit approximately between 16 and 20 kb/s. Below this limit, some of the same problems exhibited by previous transform coding techniques were present, namely, the failure to quantize certain of the transform coefficients due to a lack of a sufficient number of bits per block. Consequently, certain essential speech elements were lost. One reason for losing the essential speech elements with this early technique was that it was nonspeech specific in the sense that it did not take into account the known properties of speech, such as the all-pole vocal-tract model and the pitch model in determining the variance information and bit allocation.
In an attempt to utilize adaptive transform coding at bit rates of 16 kb/s or lower, efforts were made to develop speech specific adaption algorithms. In speech specific techniques one should account for both pitch and formant information in a speech signal. Consequently, the transform scheme utilized in an adaptive transform coder should not only produce a spectral envelope but preferably includes a modulating term which can be utilized for reflecting pitch striations.
One speech specific technique disclosed in Tribolet, J. et al. "Frequency Domain Coding of Speech" IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. ASSP-27, No. 3 (October, 1979), pp. 512-530, utilizing the DCT to obtain the transform coefficients, determined the DCT spectral envelope by first squaring the DCT coefficients and then inverse transforming the squared coefficients using an inverse DFT. The resultant time domain sample block yielded an autocorrelation-like function, which was termed the pseudo-ACF. The values of a number of initial block samples were then used to define a correlation matrix in an equation format. The solution of the equation resulted in a linear prediction model made up of linear prediction coefficients. The inverse spectrum of the linear prediction coefficients yielded a precise estimation of the DCT spectral envelope. In order to develop a pitch pattern, it was necessary to obtain a pitch period and a pitch gain. To determine these two factors, this technique searched the pseudo-ACF to determine a maximum value which became the pitch period. The pitch gain was thereafter defined as the ratio between the value of the pseudo-ACF function at the point where the maximum value was determined and the value of the pseudo-ACF at its origin. The estimated spectral envelope and the generated pitch pattern were thereafter used in conjunction with the step-size and bit assignment algorithms.
It was stated that the above speech specific technique worked better at lower bit rates, i.e. 16 kb/s, than previous adaptive transform coding techniques, because it forced the assignment of bits to many pitch harmonics, i.e. essential speech elements, which previously would not have been transmitted and it helped to preserve pitch structure information. The problem with this technique however is that due to its computational complexity, i.e. the technique required a 2N-point FFT operation, a magnitude operation, and a normalizing operation. As concluded in Crochiere, R. et al. "Real-Time Speech Coding" IEEE Transactions on Communications, Vol. COM-30, No. 4 (April, 1982), pp. 621-634 an array processor was needed for implementation. Consequently, it was not economical with regard to either processing time or cost.
Accordingly, a need still exists for an adaptive transform coder which is capable of efficient operation at low bit rates, has low noise levels, and which is capable of reasonable cost and processing time implementation.
There is also a need to design a coder which is capable of optimal performance over a wide dynamic range of input signals while maintaining a high signal-to-noise ratio at all levels. This has been attempted previously by: careful control of input levels to correctly bias A/D conversion; analog AGC prior to A/D conversion; and digital AGC after A/D conversion. Careful control of the input levels is seldom viable because most, if not all, signals come from external sources. AGC prior to A/D conversion is possible if control is maintained over the analog interface. However problems typically encountered with such procedures involve rise and fall times as well as background noise amplification. Also, inverse AGC at the receiver is not possible. Digital AGC follows the problems encountered in analog AGC and also introduces a degree of quantization noise which may not be removed.
There is still a further need for an adaptive transform coder which conducts a post bit allocation process to assure that each coefficient to be quantized is an integer. In performing bit assignment one or more calculations are used to determine the number of bits needed to quantize a particular piece of information, i.e. a transform coefficient. Such calculations do not usually yield integer numbers, but rather, result in real numbers which included an integer and a decimal fraction, e.g. 3.66, 5.72, or 2.44. If bits are only assigned to the integer portion of the calculated value and the details of the decimal fraction portions are ignored due to the limited number of available bits important information could be lost or distortion noise could be increased. Consequently, a need exists to account for the decimal fraction information and minimize the distortion noise.